In today's technology-driven society, with the rapid development and wide-ranging application of the computer's computing power and the network communication technology, especially the popularity of the Internet, human society has already stepped into the information age, and the development of the information technology is changing the traditional modes of business operation, production and life. With the advent of the information age, people want rapid and long-distance trades via digital communication networks. In such digital information world, traditional handwritten signatures and signature stamps have become difficult to work effectively, so there is an urgent need for digital signature method which provides functionality similar to the handwritten signature and signature stamp. Especially in recent years, the digital cryptography has grown greatly. There may be no internationalization of E-commerce and safe and reliable operations of the corporate infrastructure without using this technology. The digital signature can ensure the accuracy of the identity of the e-mail sender and the identity of the signer of the contract document as effective and authentic in the traditional handwritten signatures.
At present, the security of the digital signature technology relies largely on the intractability of the large integer factorization and discrete logarithm problem, such as RSA or ECC. However, such traditional digital signature technology has been under great threat since it was proposed that the method for factoring large integer and the method for solving discrete logarithm can be implemented in a quantum computer, which affects all professions and trades. Therefore, people began to find a signature scheme which can protect against quantum computer attacks to meet the requirements of the information security, and such scheme is called as post quantum signature scheme, and multivariate public key signature is one of them.
The multivariate public key signature plays an important role in the quantum signature scheme. The existing multivariable schemes are almost always insecure because of the quadratic equation in a random design having no threshold, and therefore are not available for signature and verification. For a mathematical structure generated by a corresponding center map, the center map of the mathematical structure is generally derivable (that is, the center map is not hidden), such that there is a structural problem in many multivariate signature schemes in addition to the MQ problem, and many schemes such as S flash have been completely broken. A common technique in the current multivariate signature schemes is “Large Field Technology” which maps the public key to a large field K and performs isomorphism using vectors (that is, the isomorphism is required). This approach is a double-edged sword, because the structure of K makes decryption easier, but such a structure is easy for attackers to exploit. In addition, the popular multivariate public key signature schemes include UOV and Rainbow. The signature process of the former requires only to solve a system of linear equations, so the signature is very fast. However, because of mixing the Oil variables (the number of which corresponds to the digits of the message) and the Vinegar variables in the polynomial of the private key map during the process of constructing the center map, the number of variables of the entire public key map corresponding to the private key map is very large, and the length of the public key is very long, which is disadvantage to practical application. The latter is substantially a UOV scheme with a multi-layered structure, so it is inevitable to have defects of UOV.